Analysis of Spherical Symmetries in Euclidean Spaces
By: by Claus Müller
Series: Applied Mathematical Sciences -- 129; Applied mathematical sciences (Springer-Verlag New York Inc.) -- 129.
Publisher: Springer New York
Published: 1998
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 226
ISBN-13: 9781461268277; 9781461205814
Subjects: Geometry; Mathematics; Global analysis (Mathematics); Chemistry
Description: This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. Written after many years of lecturing to mathematicians, physicists and engineers in scientific research institutions in Europe and the USA, it uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. One of the highlights of this book is the extension of the classical results of the spherical harmonics into the complex. This is particularly important for the complexification of the Funk-Hecke formula which successfully leads to new integrals for Bessel- and Hankel functions with many applications of Fourier integrals and Radon transforms. Exercises have been included to stimulate mathematical ingenuity and to bridge the gap between well known elementary results and their appearance in the new formations.
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